Paul Allen Catlin ( – ) was a mathematician, professor of mathematics who worked in

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

. He wrote a significant paper on the series of chromatic numbers and Brooks' theorem, titled '' Hajós graph coloring conjecture: variations and counterexamples''.Publication list for Paul Catlin, math.wvu.edu

Career

Originally from

Bridgeport Bridgeport is the most populous city and a major port in the U.S. state of Connecticut. With a population of 148,654 in 2020, it is also the fifth-most populous in New England. Located in eastern Fairfield County at the mouth of the Pequonnoc ...

Connecticut Connecticut () is the southernmost state in the New England region of the Northeastern United States. It is bordered by Rhode Island to the east, Massachusetts to the north, New York to the west, and Long Island Sound to the south. Its cap ...

, Catlin majored in Mathematics with a B.A. degree from

Carnegie Mellon University Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...

in 1970. Catlin held a Doctorate in Mathematics degree from

Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best publ ...

. From 1972 to 1973, he was a research and teaching assistant at

, where he earned the Master of Science degree in Mathematics. In 1976, he went to work at

Wayne State University Wayne State University (WSU) is a public research university in Detroit, Michigan. It is Michigan's third-largest university. Founded in 1868, Wayne State consists of 13 schools and colleges offering approximately 350 programs to nearly 25,000 ...

, where he concentrated the research on chromatic numbers and

Brooks' theorem In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected graph in which every vertex has at most Δ neighbors, the vertices can be colored with o ...

. As a result, Catlin published a significant paper in that series: ''Hajós graph coloring conjecture: variations and counterexamples.'', which showed that the conjecture raised by

Hugo Hadwiger Hugo Hadwiger (23 December 1908 in Karlsruhe, Germany – 29 October 1981 in Bern, Switzerland) was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography. Biography Although born in Karlsruhe, Germany, Hadwige ...

is further strengthened not only by

k \le 4

but also by

k \ge 7

, which led to the joint paper written with

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

and

Béla Bollobás Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul E ...

titled ''Hadwiger's conjecture is true for almost every graph''. He authored over fifty academic papers in

and

. Many of his contributions and collaborations have been published in ''

The Fibonacci Quarterly The ''Fibonacci Quarterly'' is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year. It is the primary publication of The Fibonacci Association, which has published it since 1963. Its founding ...

'', in '' The Journal of Number Theory'', in the ''Journal of

Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...

'', and many other academic publications. He co-authored scholarly papers with Arthur M. Hobbs,

and

, Hong-Jian Lai, Zheng-Yiao Han, and Yehong Shao, among others. He also published papers with G. Neil Robertson, with whom he also completed his dissertation thesis in 1976.

Selected publications

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References

{{DEFAULTSORT:Catlin, Paul 1948 births 1995 deaths 20th-century American mathematicians Number theorists Graph theorists Ohio State University Graduate School alumni Wayne State University faculty